Global dynamics of an intraguild predation predator-prey model with density-dependent velocity suppression

This paper investigates a diffusive predator-prey model incorporating density-dependent velocity suppression. The model consists of two reaction-diffusion equations with cross-diffusion terms characterizing predator-taxis, along with intraspecific competition and resource competition effects. The global existence and uniform boundedness of classical solutions in bounded domains Ω⊂R^N with N < 3 is established. Our results demonstrate that the density-dependent velocity suppression mechanism plays a crucial role in preventing solution blow-up and ensures the global well-posedness of the system. Furthermore, we perform a steady-state bifurcation analysis near the positive constant equilibrium and derive the conditions for the emergence of nonconstant positive steady states. The stability of bifurcating solutions is also examined. Numerical simulations in two-dimensional planar and curved domains illustrate the theoretical findings and reveal rich pattern formation, highlighting the ecological relevance of density-dependent movement in promoting species coexistence and spatial heterogeneity.